Big Idea: Observation and description of changes in the world around us
are the first steps in finding and learning about patterns.
Essential Question: What are some situations that we can describe as variable?
A. Make a coordinate graph of the (time,distance) data given in the table.
B. Sidney wants to write a report describing day 2 of our tour. Using information from the table or the graph, what could she write about the day's travel? Be sure to consider the following questions:
How far did the group travel in the day? How much time did it take them?
During which time interval(s) did the riders make the most progress? The least progress?
Did the riders go further in the first half or the second half of the day's ride?
Day 2 In 5 hours of riding our bike, we traveled 45 miles. From the starting point to 30 minutes of traveling was the most distances that we made today, and the shortest distance was between 3:30 to 4:30. On day 1 they did a better job then today. On Day 1 we rode futher out but today they didn't do the job as good on day 1.
C.
By analyzing the table,how can you find the time intervals when the riders made the most progress? The least progress? How ca you find these intervals by analyzing the graph?
You can tell that they had traveled the most between from the start to 30 minutes, because there is the most space in between then others. From 3:30 to 4:30 there is no movements, so that is how you can tell that was the one with the lest progress.
D.
Sidney wants to include either the table or the graphing her report. which do you think she should include? Why?
I think that Sidney should go with the graph, so that people will see the difference more easily.
2.2 Follow-Up
1. Look at the second point on your graph as you count from the left. We can describe this point with the coordinate pair (0.5,8). The first number in a coordinate pairs is the value for the y-coordinate. Give the coordinate pair for the third point on your graph. What information does this point give?
(1,15) In a hour they traveled 15 miles.
2. Connecting the points on a graph sometimes helps you see a pattern more clearly. You can connect the points in situations in which it makes sense to consider what is happening in the intervals between the points. The points on the graph of the data for day 3 can be connected because the riders were moving during each half- hour interval, so the distance was changing.**
Connect the points on your graph with straight line segments.
how could you use the line segments t help you estimate the distance traveled after 3/4 of an hour (0.75 hours)?
I think that it should be 11.5 miles.
3. The straight line segments you drew from (4.5,40) to (5.0,4.5) gives you some idea of how the ride might have gone between the points. It shows how the ride would have progressed if the riders had traveled at a steady rate for the entire half hour. The actual pace of the group, and of the individual riders, may have varied throughout the half hour. These paths show some possible ways the ride may have progressed:
Match each of these connecting paths with the following travel notes.
Celia rode slowly at first and gradually increased her speed.
Tony and Liz rode very quickly and reached the campsite early.
Malcolm had to fix a flat tire, so he started late.
Theo started off fast. after a while, he felt tired and slowed down.
A - ii
B - iV
C - iii
D - i
New Vocabulary
Coordinate Pair -
Coordinate pair are numbers to locate the points on a graph. The first number is the number on the X-axies, and the second number is the number on the Y-axies
September, 1, 2009
J.H.
Big Idea: Observation and description of changes in the world around us
are the first steps in finding and learning about patterns.
Essential Question: What are some situations that we can describe as variable?
A.
Make a coordinate graph of the (time,distance) data given in the table.
B.
Sidney wants to write a report describing day 2 of our tour. Using information from the table or the graph, what could she write about the day's travel? Be sure to consider the following questions:
Day 2
In 5 hours of riding our bike, we traveled 45 miles. From the starting point to 30 minutes of traveling was the most distances that we made today, and the shortest distance was between 3:30 to 4:30. On day 1 they did a better job then today. On Day 1 we rode futher out but today they didn't do the job as good on day 1.
C.
By analyzing the table,how can you find the time intervals when the riders made the most progress? The least progress? How ca you find these intervals by analyzing the graph?
You can tell that they had traveled the most between from the start to 30 minutes, because there is the most space in between then others. From 3:30 to 4:30 there is no movements, so that is how you can tell that was the one with the lest progress.
D.
Sidney wants to include either the table or the graphing her report. which do you think she should include? Why?
I think that Sidney should go with the graph, so that people will see the difference more easily.
2.2 Follow-Up
1.
Look at the second point on your graph as you count from the left. We can describe this point with the coordinate pair (0.5,8). The first number in a coordinate pairs is the value for the y-coordinate. Give the coordinate pair for the third point on your graph. What information does this point give?
(1,15) In a hour they traveled 15 miles.
2.
Connecting the points on a graph sometimes helps you see a pattern more clearly. You can connect the points in situations in which it makes sense to consider what is happening in the intervals between the points. The points on the graph of the data for day 3 can be connected because the riders were moving during each half- hour interval, so the distance was changing.**
I think that it should be 11.5 miles.
3.
The straight line segments you drew from (4.5,40) to (5.0,4.5) gives you some idea of how the ride might have gone between the points. It shows how the ride would have progressed if the riders had traveled at a steady rate for the entire half hour. The actual pace of the group, and of the individual riders, may have varied throughout the half hour. These paths show some possible ways the ride may have progressed:
Match each of these connecting paths with the following travel notes.
A - ii
B - iV
C - iii
D - i
New Vocabulary
Coordinate Pair -
Coordinate pair are numbers to locate the points on a graph. The first number is the number on the X-axies, and the second number is the number on the Y-axies